Is 512 is the perfect cube,if yes then give reason.
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Grouping the prime factors of 256 in triples, we are left over with 2 × 2. ∴ 256 is not a perfect cube. i.e. 512 is a perfect cube. ... Thus, the smallest required number to multiply 675 such that the new number perfect cube is 5.
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Yes it's a perfect cube
On prime factorisation the given number we get
512=(2×2×2)×(2×2×2)×(2×2×2)
On making triplets of 2’s we get there are 9 2’s so 2’s are making 3 triplets
Therefore 512 is a perfect cube and cube root of 512=2×2×2=8
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